Solve 1/2t+3/5=2/5-t

$$\frac { 1 } { 2 } t + \frac { 3 } { 5 } = \frac { 2 } { 5 } - t$$

Solve for t

$$t=-\frac{2}{15}\approx -0.133333333$$

Steps for Solving Linear Equation

Add t to both sides.

$$\frac{1}{2}t+\frac{3}{5}+t=\frac{2}{5}$$

Combine \frac{1}{2}t and t to get \frac{3}{2}t.

$$\frac{3}{2}t+\frac{3}{5}=\frac{2}{5}$$

Subtract \frac{3}{5} from both sides.

$$\frac{3}{2}t=\frac{2}{5}-\frac{3}{5}$$

Since \frac{2}{5} and \frac{3}{5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3}{2}t=\frac{2-3}{5}$$

Subtract 3 from 2 to get -1.

$$\frac{3}{2}t=-\frac{1}{5}$$

Multiply both sides by \frac{2}{3}, the reciprocal of \frac{3}{2}.

$$t=-\frac{1}{5}\times \frac{2}{3}$$

Multiply -\frac{1}{5} times \frac{2}{3} by multiplying numerator times numerator and denominator times denominator.

$$t=\frac{-2}{5\times 3}$$

Do the multiplications in the fraction \frac{-2}{5\times 3}.

$$t=\frac{-2}{15}$$

Fraction \frac{-2}{15} can be rewritten as -\frac{2}{15} by extracting the negative sign.

$$t=-\frac{2}{15}$$